Finite Group Databasebeta

← Group #13166525

Character table — Group #13166525

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112444448888889918181818183636362248888816161616161618183636363636727272336121212121224242424242427275454545454108108108
order12423366666612122248888244361263366666612126612242424246121222426666666612122248888244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111-1-1-1-11-1-111111111111111111-1-1-1-11-1-111111111111111111-1-1-1-11-1-1
χ311111111111111-1-1-1ii−i−i-1i−i11111111111111-1-1-1ii−i−i-1i−i11111111111111-1-1-1ii−i−i-1i−i
χ411111111111111-1-1-1−i−iii-1−ii11111111111111-1-1-1−i−iii-1−ii11111111111111-1-1-1−i−iii-1−ii
χ5111-11111-1-1-1-1111111111-1-1-1111-11111-1-1-1-1111111111-1-1-1111-11111-1-1-1-1111111111-1-1-1
χ6111-11111-1-1-1-111111-1-1-1-1-111111-11111-1-1-1-111111-1-1-1-1-111111-11111-1-1-1-111111-1-1-1-1-111
χ7111-11111-1-1-1-111-1-1-1ii−i−i1−ii111-11111-1-1-1-111-1-1-1ii−i−i1−ii111-11111-1-1-1-111-1-1-1ii−i−i1−ii
χ8111-11111-1-1-1-111-1-1-1−i−iii1i−i111-11111-1-1-1-111-1-1-1−i−iii1i−i111-11111-1-1-1-111-1-1-1−i−iii1i−i
χ922-2022220000-2-222-2000000022-2022220000-2-222-2000000022-2022220000-2-222-20000000
χ1022-2022220000-2-2-2-22000000022-2022220000-2-2-2-22000000022-2022220000-2-2-2-220000000
χ112-20022-2-20000002-20i2−i2i2−i20002-20022-2-20000002-20i2−i2i2−i20002-20022-2-20000002-20i2−i2i2−i2000
χ122-20022-2-20000002-20−i2i2−i2i20002-20022-2-20000002-20−i2i2−i2i20002-20022-2-20000002-20−i2i2−i2i2000
χ132-20022-2-2000000-2202−2−220002-20022-2-2000000-2202−2−220002-20022-2-2000000-2202−2−22000
χ142-20022-2-2000000-220−222−20002-20022-2-2000000-220−222−20002-20022-2-2000000-220−222−2000
χ1544441-21-211-2-21-2000000000044441-21-211-2-21-2000000000044441-21-211-2-21-20000000000
χ164444-21-21-2-211-2100000000004444-21-21-2-211-2100000000004444-21-21-2-211-210000000000
χ17444-41-21-2-1-1221-20000000000444-41-21-2-1-1221-20000000000444-41-21-2-1-1221-20000000000
χ18444-4-21-2122-1-1-210000000000444-4-21-2122-1-1-210000000000444-4-21-2122-1-1-210000000000
χ1944-401-21-23-300-12000000000044-401-21-23-300-12000000000044-401-21-23-300-120000000000
χ2044-401-21-2-3300-12000000000044-401-21-2-3300-12000000000044-401-21-2-3300-120000000000
χ2144-40-21-21003-32-1000000000044-40-21-21003-32-1000000000044-40-21-21003-32-10000000000
χ2244-40-21-2100-332-1000000000044-40-21-2100-332-1000000000044-40-21-2100-332-10000000000
χ238-8002-4-2400000000000000008-8002-4-2400000000000000008-8002-4-240000000000000000
χ248-800-424-200000000000000008-800-424-200000000000000008-800-424-20000000000000000
χ25111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2611111111111111111-1-1-1-11-1-111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ2711111111111111-1-1-1ii−i−i-1i−i11111111111111-1-1-1ii−i−i-1i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1111−i−iii1−ii
χ2811111111111111-1-1-1−i−iii-1−ii11111111111111-1-1-1−i−iii-1−ii-1-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i1i−i
χ29111-11111-1-1-1-1111111111-1-1-1111-11111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1111
χ30111-11111-1-1-1-111111-1-1-1-1-111111-11111-1-1-1-111111-1-1-1-1-111-1-1-11-1-1-1-11111-1-1-1-1-111111-1-1
χ31111-11111-1-1-1-111-1-1-1ii−i−i1−ii111-11111-1-1-1-111-1-1-1ii−i−i1−ii-1-1-11-1-1-1-11111-1-1111−i−iii-1i−i
χ32111-11111-1-1-1-111-1-1-1−i−iii1i−i111-11111-1-1-1-111-1-1-1−i−iii1i−i-1-1-11-1-1-1-11111-1-1111ii−i−i-1−ii
χ3322-2022220000-2-222-2000000022-2022220000-2-222-20000000-2-220-2-2-2-2000022-2-220000000
χ3422-2022220000-2-2-2-22000000022-2022220000-2-2-2-220000000-2-220-2-2-2-200002222-20000000
χ352-20022-2-20000002-20i2−i2i2−i20002-20022-2-20000002-20i2−i2i2−i2000-2200-2-222000000-220−i2i2−i2i2000
χ362-20022-2-20000002-20−i2i2−i2i20002-20022-2-20000002-20−i2i2−i2i2000-2200-2-222000000-220i2−i2i2−i2000
χ372-20022-2-2000000-2202−2−220002-20022-2-2000000-2202−2−22000-2200-2-2220000002-20−222−2000
χ382-20022-2-2000000-220−222−20002-20022-2-2000000-220−222−2000-2200-2-2220000002-202−2−22000
χ3944441-21-211-2-21-2000000000044441-21-211-2-21-20000000000-4-4-4-4-12-12-1-122-120000000000
χ404444-21-21-2-211-2100000000004444-21-21-2-211-210000000000-4-4-4-42-12-122-1-12-10000000000
χ41444-41-21-2-1-1221-20000000000444-41-21-2-1-1221-20000000000-4-4-44-12-1211-2-2-120000000000
χ42444-4-21-2122-1-1-210000000000444-4-21-2122-1-1-210000000000-4-4-442-12-1-2-2112-10000000000
χ4344-401-21-23-300-12000000000044-401-21-23-300-120000000000-4-440-12-12-33001-20000000000
χ4444-401-21-2-3300-12000000000044-401-21-2-3300-120000000000-4-440-12-123-3001-20000000000
χ4544-40-21-21003-32-1000000000044-40-21-21003-32-10000000000-4-4402-12-100-33-210000000000
χ4644-40-21-2100-332-1000000000044-40-21-2100-332-10000000000-4-4402-12-1003-3-210000000000
χ478-8002-4-2400000000000000008-8002-4-240000000000000000-8800-242-40000000000000000
χ488-800-424-200000000000000008-800-424-20000000000000000-88004-2-420000000000000000
χ49222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ5022222222222222222-2-2-2-22-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111000000000000000000000000
χ5122222222222222-2-2-22i2i−2i−2i-22i−2i-1-1-1-1-1-1-1-1-1-1-1-1-1-1111−i−iii1−ii000000000000000000000000
χ5222222222222222-2-2-2−2i−2i2i2i-2−2i2i-1-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i1i−i000000000000000000000000
χ53222-22222-2-2-2-2222222222-2-2-2-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1111000000000000000000000000
χ54222-22222-2-2-2-222222-2-2-2-2-222-1-1-11-1-1-1-11111-1-1-1-1-111111-1-1000000000000000000000000
χ55222-22222-2-2-2-222-2-2-22i2i−2i−2i2−2i2i-1-1-11-1-1-1-11111-1-1111−i−iii-1i−i000000000000000000000000
χ56222-22222-2-2-2-222-2-2-2−2i−2i2i2i22i−2i-1-1-11-1-1-1-11111-1-1111ii−i−i-1−ii000000000000000000000000
χ5744-4044440000-4-444-40000000-2-220-2-2-2-2000022-2-220000000000000000000000000000000
χ5844-4044440000-4-4-4-440000000-2-220-2-2-2-200002222-20000000000000000000000000000000
χ594-40044-4-40000004-402i2−2i22i2−2i2000-2200-2-222000000-220−i2i2−i2i2000000000000000000000000000
χ604-40044-4-40000004-40−2i22i2−2i22i2000-2200-2-222000000-220i2−i2i2−i2000000000000000000000000000
χ614-40044-4-4000000-44022−22−2222000-2200-2-2220000002-20−222−2000000000000000000000000000
χ624-40044-4-4000000-440−222222−22000-2200-2-2220000002-202−2−22000000000000000000000000000
χ6388882-42-422-4-42-40000000000-4-4-4-4-12-12-1-122-120000000000000000000000000000000000
χ648888-42-42-4-422-420000000000-4-4-4-42-12-122-1-12-10000000000000000000000000000000000
χ65888-82-42-4-2-2442-40000000000-4-4-44-12-1211-2-2-120000000000000000000000000000000000
χ66888-8-42-4244-2-2-420000000000-4-4-442-12-1-2-2112-10000000000000000000000000000000000
χ6788-802-42-46-600-240000000000-4-440-12-12-33001-20000000000000000000000000000000000
χ6888-802-42-4-6600-240000000000-4-440-12-123-3001-20000000000000000000000000000000000
χ6988-80-42-42006-64-20000000000-4-4402-12-100-33-210000000000000000000000000000000000
χ7088-80-42-4200-664-20000000000-4-4402-12-1003-3-210000000000000000000000000000000000
χ7116-16004-8-480000000000000000-8800-242-40000000000000000000000000000000000000000
χ7216-1600-848-40000000000000000-88004-2-420000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).